Inference for the entries of a Gaussian precision matrix has received a large amount of attention in the past few years, most notably post-regularization inference, for instance [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. These works generalize to the high-dimensional setup the classical ideas of one-step estimation [12]}, by first constructing a sparse estimator of the precision matrix, via regularization, and then building de-sparsified updates that are asymptotically normal. The effect of the initial regularization step is controlled in the second step, and inference after regularization becomes valid.
